Climate Change V

 

Cell Block Tango

He had it coming'
He had it coming'
He only had himself to blame
If you'd have been there
If you'd have heard it
I betcha you would have done the same

Nobody could have seen it coming?  Really?  Really?

G. W. Bush famously said that nobody could have foreseen the disaster in New Orleans caused by Hurricane Katrina and that he and FEMA Administrator Brown did a great job.  I beg to differ.  Katrina struck New Orleans on August 29, 2005.  I worked on a report for the US DOT, Impacts of Climate Variability and Change on Transportation Systems and Infrastructure- Gulf Coast Study, Department of Transportation, Washington, DC, March 2008, which studied the impact of climate change on the Gulf Coast. It studied the impact of hurricanes, their wind, rain, and storm surges, as well as sea level rises in the coastal areas of the United States from Mobile Bay, Alabama, to Galveston Bay, Texas.  That study and that geographic area were chosen in part because of an article in Scientific American, Drowning New Orleans, in the October 2001 issue which discussed the impact of a hurricane on the levees and dikes protecting New Orleans.  Katrina accidentally provided a natural experiment with which to examine and validate those methods in our study.  Also Hurricane Rita struck Houston and Galveston on September 24, 2005.  By that time evacuation plans had been developed for Houston and the success of those evacuation plans could also be evaluated.

Could anyone have predicted the date and the hour in which a hurricane would strike? No, but the impacts were known in advance. The impacts of Katrina were very much in keeping with the article in Scientific American less than 4 years earlier.  The evacuation plan for Houston called for the orderly, timed evacuation of the city in only 1 vehicle per household.  A meeting was held to evaluate the findings of the study which included the very persons who prepared the evacuation plan for Houston.  They admitted that they also had to evacuate but they used every car in their households, as many as 3 cars per household, as soon as the evacuation of any geography had begun, without waiting for their turn just like everyone else. It is any wonder that the roads during the evacuation were jammed.  IOW do as I say, not as I do.  Great job, Brownie!!! You are not to blame!!!!

Quadratic

 

Zero, My Hero

What's so wonderful about a zero? It's nothing, isn't it?
Sure, it represents nothing alone
But place a zero after one, and you've got yourself a ten
See how important that is?
When you run out of digits, you can start all over again
See how convenient that is?
That's why with only ten digits including zero
You can count as high as you could ever go
Forever, towards infinity
No one ever gets there, but you could try 

Zero is even more important than that! 

In a previous blog post  https://dbeagan.blogspot.com/2024/10/absolute-zero.html I suggested that zero as the coefficient of the imaginary part of a complex number on a hyperbolic surface is important.

The solution  of quadratic equation ax²+bx+c is typically given as x=(-b±√(b²-4ac))/(2a) if x is a real number or if x is a complex number on a Euclidean, flat, surface.  However if x is the real part of a complex number on a non-Euclidean hyperbolic surface then the quadratic equation is really ax²+bx+c+0²i and its solution is x=ln(cosh((-b±√(b²-4a*c))/(2a))±sinh((-b±√(b²-4a*c))/(2a))). Then if b²‑4a*c is negative, and its square root is imaginary, since the solution of cosh(ki) is always real but the solution of sinh(ki) is always imaginary, the solution of x will be imaginary. This is true for the period of 5/6, 83.3%, of the solutions where the traditional solution of the quadratic equation is the approximation as well as  the period of the remaining 16.7%, 1/6, where the approximation no longer applies.

The approximation means that in this case the real part will itself contradictorily be a complex number, a+b*i+0²i. For the remaining 16.7%, 1/6, the approximation will be the negative of that complex number, while the hyperbolic solution will always give the correct complex number.

For other solutions where the imaginary coefficient should always be zero, the hyperbolic solution always applies. Thus the relativistic dilation is γ=ln(cosh(√(1-v^2/c²))±sinh(√(1-v^2/c²))); Pythagoras’ Theorem is c=ln(cosh(√(a²⁺b²))±sinh(√(a²⁺b²))); in statistics the coefficient of EVERY moment about the mean is 0 not just odd moments; the real radius, r,  of a complex number, x+y*i in Cartesian coordinates translated to polar coordinates, re^iθ, is  r=ln(cosh( (√(x²⁺y²))±sinh(√(x²⁺y²))), etc. 

Hyperbolic

Three Blind Mice 

Three blind mice, three blind mice
See how they run, see how they run
They all ran after the farmer's wife
She cut off their tails with a carving knife
Did you ever see such a sight in your life as three blind mice?

In addition to blind mice, what about Blind Men and the Elephant?

The Blind Men and the Elephant is an ancient Indian parable that has roots in Buddhist, Hindu, and Jain texts, that discussed the limits of perception, and the importance of complete context, and is a poem by John Godfrey Saxe. It is also the subject of the of illustration below.

This is the phenomena that is responsible for the flat Earth Fallacy. If you use only your own perception, the Earth looks Flat, even though the Earth is a sphere. Mathematically it would be described as being locally flat, but globally spherical. If we only use our local perception it looks flat. The issue is that we are so small compared to the radius of that sphere, that it looks flat, just as the surface of a beach ball would look flat to an ant on that beach ball.  Just like the blind men who mistook the elephant as being a spear, a snake, a rope, a fan, a tree, or wall depending on what part of the elephant they were perceiving, or as Saxe’s poem goes

So oft in theological wars,
    The disputants, I ween,
Rail on in utter ignorance
    Of what each other mean,
And prate about an Elephant
    Not one of them has seen!

What we perceive as straight lines and parabolas might both only be parts of a hyperbola. A hyperbola looks like a straight line at great distances from its vertex and looks like a parabola close to its vertex. What we perceive as straight lines and parabolas in flat space might only be different parts of the same hyperbola……IOW space might be locally flat and universally hyperbolic.

That space is hyperbolic is NOT a unique idea. It was proposed by Mabkhout (Mabkhout, 2012). He pointed out that if space is hyperbolic and the Einstein field equations are solved in hyperbolic space, the need for dark matter and dark energy goes away. This is hardly the limit of this proposal. It has implications on mathematics, physics, statistics, EVERYTHING. Don’t be blind.

Mabkhout, S. (2012). The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112.

Again?

 

I Remember It Well

We met at 9
We met at 8
I was on time
No, you were late
Ah yes
I remember it well

MAGA? How well do you remember the past?

Memory is an opinion, not the Truth. That is why a jury of twelve peers is asked to judge the memory of trial witnesses, and still sometimes gets it wrong. It is why the memories of individuals can be different which is the plot of many movies such as Rashomon and the Last Duel. Memories get cloudy with age. Which is why old men since ancient Greek times have complained about the young.

What is evidence tomorrow might contradict the memory of yesterday. That is why hard evidence like written records are valued and why banning of books is so dangerous. The Texas Revolution which included the Alamo might have been fought over the ability of landowners to own slaves while the Mexican government was abolishing slavery. Wiping something from memory, such as the Tulsa Race Riot, does not mean that it did not happen, only that it is not remembered.

Before you rely on AGAIN, make sure that AGAIN is based on TRUTH and not merely on memory. Those who don’t remember the past are doomed to repeat it.

Patience

 

You Can’t Hurry Love

No, I can't bear to live my life alone
I grow impatient for a love to call my own
But when I feel that I, I can't go on
These precious words keeps me hanging on
I remember mama said
… No, you just have to wait
She said love don't come easy
It's a game of give and take

And remember to always listen to your Mama!

Goodness, we are an impatient species.  We want it right now.  But we have to remember to have patience, young padawan. You can’t hurry anything.  Being patient is NOT being boring. Settling for the first thing that comes along, not waiting to see if things change, picking the biggest thing instead of the most valuable thing shows immaturity.  Don’t be immature. Don’t hurry anything.

When I was young, comedian Alan Sherman had a hit record with Camp Granada, a parody set to the tune of the Dance of the Hours.  https://www.youtube.com/watch?v=4yFTOvO0utY.  He wrote the parody because he observed that when he sent his son to summer camp, his son wanted to come home immediately instead of giving it a chance, and his son would tell the most outrageous lies to get home.  Learning to wait, be patient, give things a chance, not to hurry anything, is just as valid today as it was when I was young.  Yes, Mama.

Election 2024 II

 

Its All In The Game

Many a tear has to fall but it's all in the game
All in the wonderful game that we know as love
You have words with him and your future's looking dim
But these things your hearts can rise above

An election is an important game, but it is still only a game.

What can Game Theory tell us about the results of an election? The outcome of any game between two equally matched contestants is win, loss AND tie. It is customary in most contests to employ some tiebreaker so that if the game ends in a tie, then it will still ultimately result  in a win or a loss. If there are two equally matched opponents it is probable that they will still have different policies and characters.

If Candidate 1 has policies that are preferred by 60% of the voters but has a character that is preferred by only 20% of the voters, then Candidate 2 must have the opposite. If wins and losses are determined by policies alone, then  Candidate 1 will win. However that is only 2/3 of the electorate. The remaining electorate, 1/3, will have to employ a tie breaker. If that tie breaker is character, then Candidate 1 will have a vote total of 47%, 60% of 2/3 plus 20% of 1/3,  while Candidate 2 will have a vote total of 53%, 40% of 2/3 plus 80% of 1/3. Candidate 2 will win. Candidate 1 may complain that only policies should have been the tie breaker or that ties should not count, but that is the math if character is the tie breaker.

That is the popular vote. The electoral vote depends on the outcome in each state weighed by its share of electoral votes. If the preference of each candidate’s policies and character differs among the electorate in each state, then the outcome in each state will be different.

The state share of electoral votes being “winner take all” is a custom only, not a constitutional requirement. If the House share of a state’s electoral votes are awarded by the vote in each House congressional district, as is the case in Nebraska, then the electoral vote will be more in keeping with the intent of the founding fathers. IOW all states should award electoral votes like Nebraska, not Nebraska should award votes by “winner takes all” like other states. Then the winning Candidate will have a majority of the voters AND broad representation among the United states.

In any event Candidate 2 should focus on character NOT policies, if character is the tie breaker. Focusing on policies alone plays to Candidate 1’s strength. Play the game correctly.

Absolute Zero

 

Key's in the Conch Shell

It's the third thatched roof on the right
Right beside crystal blue water
First wave of the day
Almost got away but my sail board caught her.

Let’s talk about that first wave.

There is a tendency to dismiss zero. But there are two kinds of zero, a relative zero and an absolute zero. An absolute zero CAN be dismissed, but a relative zero CAN NOT be dismissed. What is meant by a relative zero? Think of temperature. 0º Celsius ( 32º Fahrenheit for you non-STEM Americans) is the freezing point of water. But it is 273.15º on the absolute Kelvin temperature scale. The reason being that when measuring temperature on the Celsius scale, negative numbers are allowed. -40º Celsius means that it is cold, not that there is negative temperature. On an absolute scale there is no temperature less than zero. So there is a world of difference between a relative zero, e.g. 0º Celsius, and an absolute zero, e.g. 0º Kelvin. While it is convenient to act like ‑500º Celsius has a reality, in fact it is less than would be allowed on the Kelvin scale and thus is NOT real.

Why does this matter. A complex number is a+b*i. If b=0 is an absolute zero then it can be ignored and only the real coefficient, a, can be a concern. However if b=0 is a relative zero then it should NOT be ignored. This has a bearing on all forms of mathematics. This is because there are different solutions for linear regression, statistics, calculus, the quadratic equation, Pythagoras Theorem, relativistic dilation, etc. when that zero coefficient of an imaginary number is dropped or retained.

Pythagoras’s Theorem is c=√(a²+b²). This is true because c²=a²+b²+0²i where there is an absolute zero coefficient of the imaginary component of a complex number. But this needs imaginary solutions when a²+b² is negative. However if that zero is a relative zero and the surface is hyperbolic then the solution is c=ln(cosh(√((a²+b²))±sinh(√((a²+b²))) and no imagainary solutions are required. The hyperbolic solution is approximately √(a²+b²) most of the times that matter to us, 83.3%, 5/6, of the time. A hyperbolic solution when x is less than 16.7%, 1/6, away from the absolute will look like a parabola any way.  It is only as it nears the absolute that the approximation breaks down and it looks like a hyperbolic curved line that never approaches the absolute.

If the absolute is a wave, then it may be approximately true as you get further away from the start of that wave, even if that wave will infinitely repeat. However the approximation may break down in the first wave, before it repeats, where you are closest to the absolute. It is true that the solution to ln(cosh(x)±sinh(x)) is equal to both x and -x. However that is true only if x is larger than 1x10^-15 (at least according to Excel Microsoft Office 365 Apps version 2409)    Less than this value, the sharp discontinuity required by the approximation at x=0 appears to smooth out and the solutions are no longer equal. That first wave is different.